Context. The major challenges for a fully polarized radiative transfer driven approach
to Zeeman-Doppler imaging are still the enormous computational requirements.
In every cycle of the iterative interplay between the
forward process (spectral synthesis) and the inverse process (derivative based optimization)
the Stokes profile synthesis requires several thousand evaluations of the
polarized radiative transfer equation for a given stellar surface model.

Aims. To cope with these computational demands and to allow for
the incorporation of a full Stokes profile synthesis
into Doppler- and Zeeman-Doppler imaging applications as well as into
large scale solar Stokes profile inversions,
we present a novel fast and accurate
synthesis method for calculating local Stokes profiles.

Methods. Our approach is based on artificial neural network models, which we use to
approximate the complex non-linear mapping between the most important
atmospheric parameters and the corresponding Stokes profiles.
A number of specialized artificial neural networks, are
used to model the functional relation between the model atmosphere,
magnetic field strength, field inclination, and field azimuth, on one hand
and the individual components of the Stokes profiles, on the other hand.

Results. We performed an extensive statistical evaluation and show that
our new approach yields accurate local as well as disk-integrated Stokes profiles
over a wide range of atmospheric conditions. The mean rms errors for the Stokes I
and V profiles are well below 0.2% compared to the exact numerical solution.
Errors for Stokes Q and U are in the range of 1%. Our approach does not only offer
an accurate approximation to the LTE polarized radiative transfer
it, moreover, accelerates the synthesis by a factor of more than 1000.

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